Dynamic dampers (dynamic vibration absorbers) have widely been used to reduce the vibration of machines. The dynamic damper is a component constituted by a mass and a spring having the same proper frequency as the frequency of a subject vibration. The dynamic damper reduces a subject vibration as a result of vibrating 180° out of phase with the subject vibration and also by utilizing the inertia of the mass.
The proper frequency (natural frequency) f is expressed by:f=ω/2π=(½π)√(K/M)where ω is a proper value, K is a spring constant, and M is a mass.
A typical dynamic damper reduces a subject vibration as a result of vibrating 180° out of phase with the subject vibration at a proper frequency f determined by the ratio of a spring constant K to a mass M and also by utilizing the inertia of the mass M. Consequently, one dynamic damper is required for one frequency. The use of plural dynamic dampers having close proper frequencies f may cause the interference of vibrations and even increase the vibrations.
A dynamic damper may be used for reducing noise caused by the vibration of an engine. In this case, the frequency of the vibration may vary in synchronization with the engine speed, and the dynamic damper may have to deal with plural frequencies.
To handle such a situation, a dynamic damper that can make the proper frequency f variable by using a magnetorheological elastomer (MRE) as a spring has been proposed (see, for example, International Publication No. 2012-026332). In such a dynamic damper, the strength of magnetic fields generated by a current flowing through a coil and applied to rubber mixed with a magnetic body is controlled, thereby making the stiffness of the rubber variable.
Typically, such a variable dynamic damper using MRE is controlled by reading a current value from a preset correlation table in which current values and rubber stiffness values are associated with each other. However, the spring constant of rubber varies according to the temperature and also changes over time. The properties of rubber are also different depending on the manufacturing variations. It is thus difficult to achieve the long-term stability and effectiveness in controlling such a dynamic damper.
In view of this background, the following control method for adjusting the frequency of a dynamic damper has been proposed (see, for example, Japanese Unexamined Patent Application Publication No. 2016-1008). By using a vibration detector for detecting the vibration of a movable mass, a displacement detector for detecting the displacement of a spring, and a frequency detector for detecting the frequency (such as an engine speed signal) to determine the frequency for reducing the vibration, the frequency of a dynamic damper is caused to follow the detected frequency.
This control method will be discussed more specifically. The equation of motion of the mass M is expressed by:Ma=−KX where a is the acceleration and X is the displacement of a spring (spring constant K). This equation can be modified into:a/X−−(K/M)
The proper value f is expressed by:f=(½π)√(K/M).
That is, the ratio of the vibration acceleration of the movable mass to the displacement of the spring is proportional to the square of the proper value of the mass M and the spring (spring constant K). By using this theory, f2 (the square of the detected frequency f of the engine) and |a/X| are successively compared with each other. If f2 is smaller than |a/X|, the spring constant K is increased by ΔK (the current applied to the coil is increased). If f2 is greater than |a/X|, the spring constant K is decreased by ΔK (the current applied to the coil is decreased).